\section{Conclusion}
We present a one-pass 5.45-approximation algorithm for the maximum
matching problem on the semi-streaming model. Our analysis of the
algorithm has the potential to be extended further.

The main open problem is to improve the approximation factor from
5.45. There are two possible approaches. The first way is to extend
the algorithm presented here by examining the whole sequence of
edges in the matching and the shadow-edges (instead of just seven
edges as in this algorithm). The other way is to give a tighter
analysis of Algorithm~\ref{alg:shadow_algorithm}. We believe that
our analysis is the first step toward these directions.
